The New Jersey winner of the massive Mega Millions jackpot advertised as being worth $1.13 billion is in for some sticker shock on the tax bill. The final take home amount will likely be staggeringly lower. To begin with, the cash option of the final jackpot — actually $1.128 billion per Mega Millions officials — is worth $536.6 million. With only the rarest of exceptions, jackpot winners have overwhelmingly chosen the cash lump sum option rather than the annual payments. Then the IRS gets a big bite — 24% — or more than $128.7 million according to the New Jersey Lottery. Finally, New Jersey r…